Story highlights

Chris Christie is advocating a bigger U.S. role in Syria, while Donald Trump says the United States should stay out of the country

Their comments come after Russian President Vladimir Putin started air strikes in Syria

Washington (CNN)Donald Trump says the United States should let Russia intervene in Syria all it wants. But Chris Christie is calling for a bigger U.S. role.

The two Republican presidential candidates' Sunday comments come as Russian President Vladimir Putin pushes forward with air strikes in Syria -- though it appears he's targeting not just ISIS fighters but U.S.-supported Syrian rebels who are fighting against Syrian President Bashar al-Assad's government.

"Now that he's there, America's got to re-establish its presence in that area," Christie said on ABC's "This Week." "We should be the ones leading the fight on ISIS. And by the way, we know Putin's not fighting ISIS. Putin's there to prop up Assad."

Trump's take? Leave ISIS to Putin.

"We're bogged down," Trump said on NBC's "Meet the Press." "Russia was bogged down in Afghanistan, meaning the Soviet Union. It broke up the Soviet Union. They're going to get bogged down, you watch."

Read More

The conflicting opinions between Trump and Christie on the proper approach to combating ISIS highlights an internal divide within the GOP when it comes to foreign policy. Some presidential candidates, like Sen. Lindsey Graham, Sen. Marco Rubio and former Sen. Rick Santorum have advocated for a more heavy-handed approach, while others, such as Sen. Rand Paul, have advocated policies aimed at avoiding getting further mired in the region.

Trump said that removing Assad from power would be a bad move -- and said removing Saddam Hussein from power in Iraq was a mistake, too, that created chaos.

"We are fighting Assad. And we're fighting for people and helping people that we don't even know who they are. And they may be worse than Assad," he said. "They may be worse, OK?"

He also predicted that Putin would run into problems like the United States has in past Middle Eastern excursions.

"I'm not just justifying Putin," Trump said. "But you watch, he'll get bogged down there. He'll be there. He'll spend a fortune. He'll be begging to get out. Everybody that's gone to the Middle East has had nothing but problems."

Christie called Trump's position "painfully naive" and compared him to President Barack Obama.

He also said he'd impose a no-fly zone over the country.

"There's now 300,000 nearly dead in Syria because of Assad and now Putin is going in and teaming with the Iranians to prop up Assad," Christie said.

"Only Barack Obama and Hillary Clinton could mess up this foreign policy that badly," he said. "And anybody who agrees with allowing the Russians into the Middle East is just painfully naive."